function [x,y] = euler(f,x0,y0,x1,n)
% Use Euler's method to solve the initial value problem
% for the first order ODE
% yprime = f(x,y), y(x0) = y0
% over the interval [x0,x1]
% Calling sequence
% function [x,y] = euler(f,x0,y0,x1,n)
% Kartik's MATLAB code
% August 20, 2005

xbar = x0;
ybar = y0;
x = xbar;
y = ybar;
% Compute the step
h = (x1-x0)/n;
for i=1:n, 
    ybar = ybar + h*f(xbar,ybar);
    xbar = xbar + h;
    y = [y; ybar];
    x = [x; xbar];
end